Place the cucumber slices in a colander set in the sink.
Pour the vinegar and 2 teaspoons of the salt over them.
Drain for at least 20 minutes, then remove the cucumber slices from the colander and pat dry.
In the bowl of a food processor fitted with the metal blade, combine the cream cheese, butter, garlic, green onions, lemon juice, lemon zest, the remaining 1 teaspoon salt, the pepper, and dill.
Process until the mixture is smooth.
Cut into the bread slices with a 2-inch round cookie cutter.
Place the rounds in an airtight zip-top bag until you're ready to assemble the sandwiches.
Spread the cream cheese mixture on the bread slices.
Top with cucumber slices and garnish with a sprig of fresh dill.
Serve immediately.